I don't know its equivalent in other languages, but it's when you take a day off without prior notice (like لا قدَّر الله when you wake up in the morning too sick to get up, or too late to be able to reach work on time) so you phone your boss and tell him you'll need to take the day off.

And أجازة عارضة (as we call it in Egypt) is just one day. If a person needs more days, then it's either [dis]counted from his yearly vacation days, or from his أجازات مرضية (sick leaves).

Hello everyone
Why I think it should be "a day-off taken because of an accident" ? Well, "عرضية" is derived from "عَرَض" and thus should have the meaning of "casual", "temporary", "not lasting". "عطلة" on the other hand entails the idea of temporariness ; "عرضية" is added to "عطلة" to emphasize temporariness. To conclude, "عطلة عرضية" is something brief and its equivalent in Arabic must be "a day-off taken because of an accident".

Though the difference between a sick leave and an 'unforeseen leave' is unclear to me. I mean, usually a sick leave is taken after you fall ill, so your employer doesn't know until the morning you don't come, right?

Yes, the difference is just technical.
A sick leave can extend to more than one day. So we can say that if a person is sick, he can ask for a عطلة عرضية/ أجازة عارضة and if doesn't get better the next day, he'll need to provide a certificate from a doctor stating that he is indeed sick and needs X days off.

So workplaces do not have أجازة عارضة/عطلة عرضية and the unplanned one-day off is deduced from the workers sick leaves.

Hello everyone
Why I think it should be "a day-off taken because of an accident" ? Well, "عرضية" is derived from "عَرَض" and thus should have the meaning of "casual", "temporary", "not lasting". "عطلة" on the other hand entails the idea of temporariness ; "عرضية" is added to "عطلة" to emphasize temporariness. To conclude, "عطلة عرضية" is something brief and its equivalent in Arabic must be "a day-off taken because of an accident".

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Didn't write my idea correctly, it should be : "and it could be an equivalent of "a day-off taken because of an accident".